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There is no enough room here to write the answer to your question. However, you can take a look at the appendix of Hartshorne and if you have time, a classical reference is Griffiths and Harris: Principles in algebraic geometry. However roughly speaking, the concept of positivity will tell you that when a compact Kahler complex manifold is algebraic.

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There is no enough room here to write the answer to your question. However, you can take a look at the appendix of Hartshorne and if you have time, a classical reference is Griffiths and Harris: Principles in algebraic geometry. However roughly speaking, the concept of positivity will tell you that a compact Kahler complex manifold is algebraic.